A Note on the Estimate of Treatment Effect from a Cox Regression Model When the Proportionality Assumption Is Violated

• Published in: Communications in statistics. Theory and methods Vol. 35; no. 3; pp. 521 - 526
• Main Authors: Joshua Chen, Y. H., Frank Liu, G. H.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01-04-2006; Taylor & Francis
• Subjects: Applications; Cox proportional hazards model; Crossing hazards; Exact sciences and technology; Mathematics; Maximum likelihood estimator; Medical sciences; Multivariate analysis; Nonparametric inference; Primary 62 (Statistics); Probability and statistics; Proportionality; Qualitative; Sciences and techniques of general use; Secondary 62N (Survival analysis and censored data); Statistics; Censored data; Data analysis; Proportionality; Treatment efficiency; Mean estimation; Secondary 62N (Survival analysis and censored data); Cox proportional hazards model; Statistical method; Crossing hazards; Maximum likelihood estimator; Survival analysis; Qualitative. Primary 62 (Statistics); Cox model; Model matching; Regression model; Maximum likelihood; Sample survey; Survival data
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610920500476671

Cox proportional hazards regression model has been widely used to estimate the effect of a prognostic factor on a time-to-event outcome. In a survey of survival analyses in cancer journals, it was found that only 5% of studies using Cox proportional hazards model attempted to verify the underlying assumption. Usually an estimate of the treatment effect from fitting a Cox model was reported without validation of the proportionality assumption. It is not clear how such an estimate should be interpreted if the proportionality assumption is violated. In this article, we show that the estimate of treatment effect from a Cox regression model can be interpreted as a weighted average of the log-scaled hazard ratio over the duration of study. A hypothetic example is used to explain the weights.